Pub Date : 2021-02-25DOI: 10.1080/17415977.2021.1890068
F. Kanca, İ. Bağlan
In this work, two-dimensional inverse quasi-linear parabolic problem with periodic boundary and integral overdetermination conditions is investigated. The formal solution is obtained by the Fourier approximation. Under some natural regularity and consistency conditions on the input data,the existence, uniqueness and continuously dependence upon the data of the solution are proved by iteration method. The inverse problem is first examined by linearization and then used implicit finite difference scheme for the numerical solution. Also predictor corrector method is considered in the numerical approach. Some results on the numerical solution with two examples are presented with figures and tables. The sensitivity of the scheme with respect to noisy overdetermination data is illustrated.
{"title":"Analysis for two-dimensional inverse quasilinear parabolic problem by Fourier method","authors":"F. Kanca, İ. Bağlan","doi":"10.1080/17415977.2021.1890068","DOIUrl":"https://doi.org/10.1080/17415977.2021.1890068","url":null,"abstract":"In this work, two-dimensional inverse quasi-linear parabolic problem with periodic boundary and integral overdetermination conditions is investigated. The formal solution is obtained by the Fourier approximation. Under some natural regularity and consistency conditions on the input data,the existence, uniqueness and continuously dependence upon the data of the solution are proved by iteration method. The inverse problem is first examined by linearization and then used implicit finite difference scheme for the numerical solution. Also predictor corrector method is considered in the numerical approach. Some results on the numerical solution with two examples are presented with figures and tables. The sensitivity of the scheme with respect to noisy overdetermination data is illustrated.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1912 - 1945"},"PeriodicalIF":1.3,"publicationDate":"2021-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1890068","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43649244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-24DOI: 10.1080/17415977.2021.1887172
B. Jackson, J. Connolly, R. Gerlach, I. Klapper, A. Parker
ABSTRACT Urea-hydrolysing biofilms are crucial to applications in medicine, engineering, and science. Quantitative information about ureolysis rates in biofilms is required to model these applications. We formulate a novel model of urea consumption in a biofilm that allows different kinetics, for example either first order or Michaelis–Menten. The model is fit to synthetic data to validate and compare two approaches, Bayesian and nonlinear least squares (NLS), commonly used by biofilm practitioners. The shortcomings of NLS motivate the Bayesian approach where a simple Markov Chain Monte Carlo (MCMC) sampler is applied. The model is then fit to real data of influent and effluent urea concentrations from experiments with biofilms of Escherichia coli. Results from synthetic data aid in interpreting results from real data, where first-order and Michaelis–Menten kinetic models are compared. The method shows potential for general applications requiring biofilm kinetic information.
{"title":"Bayesian estimation and uncertainty quantification in models of urea hydrolysis by E. coli biofilms","authors":"B. Jackson, J. Connolly, R. Gerlach, I. Klapper, A. Parker","doi":"10.1080/17415977.2021.1887172","DOIUrl":"https://doi.org/10.1080/17415977.2021.1887172","url":null,"abstract":"ABSTRACT Urea-hydrolysing biofilms are crucial to applications in medicine, engineering, and science. Quantitative information about ureolysis rates in biofilms is required to model these applications. We formulate a novel model of urea consumption in a biofilm that allows different kinetics, for example either first order or Michaelis–Menten. The model is fit to synthetic data to validate and compare two approaches, Bayesian and nonlinear least squares (NLS), commonly used by biofilm practitioners. The shortcomings of NLS motivate the Bayesian approach where a simple Markov Chain Monte Carlo (MCMC) sampler is applied. The model is then fit to real data of influent and effluent urea concentrations from experiments with biofilms of Escherichia coli. Results from synthetic data aid in interpreting results from real data, where first-order and Michaelis–Menten kinetic models are compared. The method shows potential for general applications requiring biofilm kinetic information.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1629 - 1652"},"PeriodicalIF":1.3,"publicationDate":"2021-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1887172","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41889341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-22DOI: 10.1080/17415977.2020.1870973
P. C. Pontes, J. M. C. Junior, C. Naveira-Cotta, Mrigank Tiwari
This work advances the approximation error model approach for the inverse analysis of the biodiesel synthesis using soybean oil and methanol in 3D-microreactors. Two hybrid numerical-analytical approaches of reduced computational cost are considered to offer an approximate forward problem solution for a three-dimensional nonlinear coupled diffusive-convective-reactive model. First, the Generalized Integral Transform Technique (GITT) is applied using approximate non-converged solutions of the 3D model, by adopting low truncation orders in the eigenfunction expansions. Second, the Coupled Integral Equations Approach (CIEA) provides a reduced mathematical model for the average concentrations, which leads to inherently approximate solutions. The AEM approach through the Bayesian framework is illustrated in the simultaneous estimation of kinetic and diffusion coefficients of the transesterification reaction. For this purpose, the fully converged GITT results with higher truncation orders for the 3D partial differential model are employed as reference results to define the approximations errors. The results highlight that either the non-converged solutions via GITT or the reduced model solution obtained via CIEA, when taking into account the model error, are robust and cost-effective alternatives for the inverse analysis of nonlinear convection–diffusion-reaction problems.
{"title":"Approximation error model (AEM) approach with hybrid methods in the forward-inverse analysis of the transesterification reaction in 3D-microreactors","authors":"P. C. Pontes, J. M. C. Junior, C. Naveira-Cotta, Mrigank Tiwari","doi":"10.1080/17415977.2020.1870973","DOIUrl":"https://doi.org/10.1080/17415977.2020.1870973","url":null,"abstract":"This work advances the approximation error model approach for the inverse analysis of the biodiesel synthesis using soybean oil and methanol in 3D-microreactors. Two hybrid numerical-analytical approaches of reduced computational cost are considered to offer an approximate forward problem solution for a three-dimensional nonlinear coupled diffusive-convective-reactive model. First, the Generalized Integral Transform Technique (GITT) is applied using approximate non-converged solutions of the 3D model, by adopting low truncation orders in the eigenfunction expansions. Second, the Coupled Integral Equations Approach (CIEA) provides a reduced mathematical model for the average concentrations, which leads to inherently approximate solutions. The AEM approach through the Bayesian framework is illustrated in the simultaneous estimation of kinetic and diffusion coefficients of the transesterification reaction. For this purpose, the fully converged GITT results with higher truncation orders for the 3D partial differential model are employed as reference results to define the approximations errors. The results highlight that either the non-converged solutions via GITT or the reduced model solution obtained via CIEA, when taking into account the model error, are robust and cost-effective alternatives for the inverse analysis of nonlinear convection–diffusion-reaction problems.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1586 - 1612"},"PeriodicalIF":1.3,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1870973","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44754425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-17DOI: 10.1080/17415977.2021.1872565
M. Hashemi, R. Izadifard, O. Yazdanpanah
In this research work, a crack diagnosis method for beam-column structures is proposed considering axial load effects through experimental data. The proposed method is employed for the detection of damage locations including single and multiple damage scenarios considering four cases of simply supported beam-column. The results show that the locations of single and multiple damage scenarios can be well recognized in low axial loads considering random noise effect. However, in the vicinity of the critical load, healthy and damaged static data are uncommon. On the other hand, increasing the axial load, especially when it reaches to the critical load, has a negative effect on the static responses that is precisely considered by the proposed damaged index.
{"title":"Experimental static data based damage localization of beam-like structures considering axial load","authors":"M. Hashemi, R. Izadifard, O. Yazdanpanah","doi":"10.1080/17415977.2021.1872565","DOIUrl":"https://doi.org/10.1080/17415977.2021.1872565","url":null,"abstract":"In this research work, a crack diagnosis method for beam-column structures is proposed considering axial load effects through experimental data. The proposed method is employed for the detection of damage locations including single and multiple damage scenarios considering four cases of simply supported beam-column. The results show that the locations of single and multiple damage scenarios can be well recognized in low axial loads considering random noise effect. However, in the vicinity of the critical load, healthy and damaged static data are uncommon. On the other hand, increasing the axial load, especially when it reaches to the critical load, has a negative effect on the static responses that is precisely considered by the proposed damaged index.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1729 - 1745"},"PeriodicalIF":1.3,"publicationDate":"2021-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1872565","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47822838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-09DOI: 10.1080/17415977.2021.1886290
Bo Chen, Yao Sun
This paper investigates the approximate solutions to the time-dependent acoustic scattering problem with a point-like scatterer under some basic assumptions and provides a simple method to reconstruct the location of the scatterer. The approximations of the solution to the forward scattering problem are analysed utilizing Green's function and the retarded single-layer potential. Then, based on the approximate solutions, a sampling method is proposed to solve the inverse scattering problem for the location of the scatterer. The proposed method is easy to implement since no equations or matrices have to be computed for the reconstruction. Numerical experiments are provided to show the effectiveness of the method.
{"title":"A simple method of reconstructing a point-like scatterer according to time-dependent acoustic wave propagation","authors":"Bo Chen, Yao Sun","doi":"10.1080/17415977.2021.1886290","DOIUrl":"https://doi.org/10.1080/17415977.2021.1886290","url":null,"abstract":"This paper investigates the approximate solutions to the time-dependent acoustic scattering problem with a point-like scatterer under some basic assumptions and provides a simple method to reconstruct the location of the scatterer. The approximations of the solution to the forward scattering problem are analysed utilizing Green's function and the retarded single-layer potential. Then, based on the approximate solutions, a sampling method is proposed to solve the inverse scattering problem for the location of the scatterer. The proposed method is easy to implement since no equations or matrices have to be computed for the reconstruction. Numerical experiments are provided to show the effectiveness of the method.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1895 - 1911"},"PeriodicalIF":1.3,"publicationDate":"2021-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1886290","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47555066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-09DOI: 10.1080/17415977.2021.1884246
Khaled M. Elmorabie, Rania R. Yahya
ABSTRACT This work is devoted to studying a direct and inverse scattering problem for a magnetoelastic layer having a defect, in the frame of the electromagnetic theory. In terms of the displacement field over the defect's contour, a coupled system of boundary integral equations is formulated, for magnetically permeable and impermeable defects. To identify the position and size of the defect, an efficient numerical algorithm is developed by using the quasi-Newton iterative method. In order to check the influence of the magnetic field upon the scattering waves from the layer, a series of numerical examples is presented with different noise levels. The results showed that the magnetic field has a sensitive effect on the identification process when the external magnetic field increases, especially for the materials having a high magnetic permeability factor . Also, a special inverse problem for predicting the external applied magnetic field, upon a copper layer having a defect with various sizes, has been performed.
{"title":"Inverse scattering problem for detecting a defect in a magnetoelastic layer","authors":"Khaled M. Elmorabie, Rania R. Yahya","doi":"10.1080/17415977.2021.1884246","DOIUrl":"https://doi.org/10.1080/17415977.2021.1884246","url":null,"abstract":"ABSTRACT This work is devoted to studying a direct and inverse scattering problem for a magnetoelastic layer having a defect, in the frame of the electromagnetic theory. In terms of the displacement field over the defect's contour, a coupled system of boundary integral equations is formulated, for magnetically permeable and impermeable defects. To identify the position and size of the defect, an efficient numerical algorithm is developed by using the quasi-Newton iterative method. In order to check the influence of the magnetic field upon the scattering waves from the layer, a series of numerical examples is presented with different noise levels. The results showed that the magnetic field has a sensitive effect on the identification process when the external magnetic field increases, especially for the materials having a high magnetic permeability factor . Also, a special inverse problem for predicting the external applied magnetic field, upon a copper layer having a defect with various sizes, has been performed.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1864 - 1894"},"PeriodicalIF":1.3,"publicationDate":"2021-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1884246","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43317548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-08DOI: 10.1080/17415977.2021.1879804
Hairui Zhang, Yongxin Yuan
A discrete gyroscopic system is characterized by first-order ordinary differential equations defined by one symmetric and one skew-symmetric, which system describes the motion of a spinning body containing elastic parts. In this paper, we consider the inverse problems of such system: Given partial spectral data, find a system such that it is of the desired spectral data. The general solution of the problem is given and the best approximation solution to a pair of matrices is provided by QR-decomposition and matrix derivation. In addition, we also consider a special case in which the system operates below the lowest critical speed. The numerical examples show that the proposed method is effective.
{"title":"Inverse eigenvalue problems for discrete gyroscopic systems","authors":"Hairui Zhang, Yongxin Yuan","doi":"10.1080/17415977.2021.1879804","DOIUrl":"https://doi.org/10.1080/17415977.2021.1879804","url":null,"abstract":"A discrete gyroscopic system is characterized by first-order ordinary differential equations defined by one symmetric and one skew-symmetric, which system describes the motion of a spinning body containing elastic parts. In this paper, we consider the inverse problems of such system: Given partial spectral data, find a system such that it is of the desired spectral data. The general solution of the problem is given and the best approximation solution to a pair of matrices is provided by QR-decomposition and matrix derivation. In addition, we also consider a special case in which the system operates below the lowest critical speed. The numerical examples show that the proposed method is effective.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1746 - 1763"},"PeriodicalIF":1.3,"publicationDate":"2021-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1879804","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42770920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-05DOI: 10.1080/17415977.2021.1880398
Jesse Adams, M. Morzfeld, K. Joyce, M. Howard, A. Luttman
ABSTRACT Among the most significant challenges with using Markov chain Monte Carlo (MCMC) methods for sampling from the posterior distributions of Bayesian inverse problems is the rate at which the sampling becomes computationally intractable, as a function of the number of estimated parameters. In image deblurring, there are many MCMC algorithms in the literature, but few attempt reconstructions for images larger than pixels ( parameters). In quantitative X-ray radiography, used to diagnose dynamic materials experiments, the images can be much larger, leading to problems with millions of parameters. We address this issue and construct a Gibbs sampler via a blocking scheme that leads to a sparse and highly structured posterior precision matrix. The Gibbs sampler naturally exploits the special matrix structure during sampling, making it ‘dimension-robust’, so that its mixing properties are nearly independent of the image size, and generating one sample is computationally feasible. The dimension-robustness enables the characterization of posteriors for large-scale image deblurring problems on modest computational platforms. We demonstrate applicability of this approach by deblurring radiographs of size pixels ( parameters) taken at the Cygnus Dual Beam X-ray Radiography Facility at the U.S. Department of Energy's Nevada National Security Site.
{"title":"A blocking scheme for dimension-robust Gibbs sampling in large-scale image deblurring","authors":"Jesse Adams, M. Morzfeld, K. Joyce, M. Howard, A. Luttman","doi":"10.1080/17415977.2021.1880398","DOIUrl":"https://doi.org/10.1080/17415977.2021.1880398","url":null,"abstract":"ABSTRACT Among the most significant challenges with using Markov chain Monte Carlo (MCMC) methods for sampling from the posterior distributions of Bayesian inverse problems is the rate at which the sampling becomes computationally intractable, as a function of the number of estimated parameters. In image deblurring, there are many MCMC algorithms in the literature, but few attempt reconstructions for images larger than pixels ( parameters). In quantitative X-ray radiography, used to diagnose dynamic materials experiments, the images can be much larger, leading to problems with millions of parameters. We address this issue and construct a Gibbs sampler via a blocking scheme that leads to a sparse and highly structured posterior precision matrix. The Gibbs sampler naturally exploits the special matrix structure during sampling, making it ‘dimension-robust’, so that its mixing properties are nearly independent of the image size, and generating one sample is computationally feasible. The dimension-robustness enables the characterization of posteriors for large-scale image deblurring problems on modest computational platforms. We demonstrate applicability of this approach by deblurring radiographs of size pixels ( parameters) taken at the Cygnus Dual Beam X-ray Radiography Facility at the U.S. Department of Energy's Nevada National Security Site.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"1789 - 1810"},"PeriodicalIF":1.3,"publicationDate":"2021-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1880398","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47491214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-03DOI: 10.1080/17415977.2021.1876688
S. Rakshit, B. Datta
ABSTRACT The structured partial quadratic inverse eigenvalue problem (SPQIEP) is to construct the structured quadratic matrix polynomial using the partial eigendata. The structures arising in physical applications include symmetry, band (tridiagonal, diagonal, pentagonal) etc. The construction of the structured matrix polynomial is the most difficult aspect of this problem and the research on structured inverse eigenvalue problem is rare. In this paper, the symmetric band partial quadratic inverse eigenvalue problem (SBPQIEP) for the damped mass spring system is considered. This problem concerns in finding the symmetric band matrices , and C with bandwidth p from m ( ) prescribed eigenpairs so that the corresponding quadratic matrix polynomial has the given eigenpairs as its eigenvalues and eigenvectors. In general, SBPQIEP is very hard to solve due to the additional band structure constraint. We propose a novel method, based on the matrix-vectorization and Kronecker product of matrices for solving this problem. Furthermore, explicit expressions for general solutions are presented. Numerical experiments on a spring mass problem are presented to illustrate the applicability and the practical usefulness of the proposed method.
{"title":"Solution of the symmetric band partial inverse eigenvalue problem for the damped mass spring system","authors":"S. Rakshit, B. Datta","doi":"10.1080/17415977.2021.1876688","DOIUrl":"https://doi.org/10.1080/17415977.2021.1876688","url":null,"abstract":"ABSTRACT The structured partial quadratic inverse eigenvalue problem (SPQIEP) is to construct the structured quadratic matrix polynomial using the partial eigendata. The structures arising in physical applications include symmetry, band (tridiagonal, diagonal, pentagonal) etc. The construction of the structured matrix polynomial is the most difficult aspect of this problem and the research on structured inverse eigenvalue problem is rare. In this paper, the symmetric band partial quadratic inverse eigenvalue problem (SBPQIEP) for the damped mass spring system is considered. This problem concerns in finding the symmetric band matrices , and C with bandwidth p from m ( ) prescribed eigenpairs so that the corresponding quadratic matrix polynomial has the given eigenpairs as its eigenvalues and eigenvectors. In general, SBPQIEP is very hard to solve due to the additional band structure constraint. We propose a novel method, based on the matrix-vectorization and Kronecker product of matrices for solving this problem. Furthermore, explicit expressions for general solutions are presented. Numerical experiments on a spring mass problem are presented to illustrate the applicability and the practical usefulness of the proposed method.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"11 1","pages":"1497 - 1518"},"PeriodicalIF":1.3,"publicationDate":"2021-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2021.1876688","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59998275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-01DOI: 10.1080/17415977.2020.1781848
Zhen Chen, Zhen Wang, Zhihao Wang, T. Chan
The studies on inverse problems exist extensively in aerospace, mechanical, identification, detection, scanning imaging and other fields. Its ill-posed characteristics often lead to large oscillations in the solution of the inverse problem. In this study, the truncated generalized singular value decomposition (TGSVD) method is introduced to identify two kinds of moving forces, single and multi-axial forces. The truncating point is the most influential regularization parameter of TGSVD, which is initially selected by two classic regularization parameter selection criteria, namely, the L-curve criterion and the generalized cross-validation (GCV) criterion. Due to numerical non-uniqueness and noise disturbance in moving force identification (MFI), numerical simulation results show that neither of the two criteria can effectively help select the optimal truncating point of TGSVD. Hence, a relative percentage error (RPE) criterion is proposed for selecting the truncating point of TGSVD. Comparative studies show that the RPE criterion can be used to select the optimal truncating point of TGSVD more accurately against the GCV criterion and L-curve criterion. Moreover, the RPE criterion can be used to reflect the connections between certain properties and the ill-posedness problem existing in MFI, which should be adopted priority for the optimal truncating point selection of TGSVD.
{"title":"Comparative studies on the criteria for regularization parameter selection based on moving force identification","authors":"Zhen Chen, Zhen Wang, Zhihao Wang, T. Chan","doi":"10.1080/17415977.2020.1781848","DOIUrl":"https://doi.org/10.1080/17415977.2020.1781848","url":null,"abstract":"The studies on inverse problems exist extensively in aerospace, mechanical, identification, detection, scanning imaging and other fields. Its ill-posed characteristics often lead to large oscillations in the solution of the inverse problem. In this study, the truncated generalized singular value decomposition (TGSVD) method is introduced to identify two kinds of moving forces, single and multi-axial forces. The truncating point is the most influential regularization parameter of TGSVD, which is initially selected by two classic regularization parameter selection criteria, namely, the L-curve criterion and the generalized cross-validation (GCV) criterion. Due to numerical non-uniqueness and noise disturbance in moving force identification (MFI), numerical simulation results show that neither of the two criteria can effectively help select the optimal truncating point of TGSVD. Hence, a relative percentage error (RPE) criterion is proposed for selecting the truncating point of TGSVD. Comparative studies show that the RPE criterion can be used to select the optimal truncating point of TGSVD more accurately against the GCV criterion and L-curve criterion. Moreover, the RPE criterion can be used to reflect the connections between certain properties and the ill-posedness problem existing in MFI, which should be adopted priority for the optimal truncating point selection of TGSVD.","PeriodicalId":54926,"journal":{"name":"Inverse Problems in Science and Engineering","volume":"29 1","pages":"153 - 173"},"PeriodicalIF":1.3,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/17415977.2020.1781848","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42279517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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